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Robert James Campbell (inset) is set to die for the abduction and murder of Alexandra Rendon in Houston in 1991.

The U.S. Supreme Court on Monday refused an appeal from a Texas death row inmate whose attorneys had demanded that state officials disclose the source of drugs intended to execute him.

Robert James Campbell, 41, had avoided execution May 13 when the 5th U.S. Circuit Court of Appeals stopped his punishment less than three hours before he could have been put to death. That court agreed to give Campbell's lawyers time to pursue their claims that he's mentally impaired and ineligible for the death penalty. That issue is still pending.

At the time of the reprieve, Campbell's appeal seeking identity of the supplier of the pentobarbital used by the Texas Department of Criminal Justice for executions was before the Supreme Court.

Campbell was sentenced to death for the 1991 abduction, rape and slaying of a 20-year-old Houston bank teller, Alexandra Rendon.

The ruling, one of three Monday involving condemned Texas prisoners, was in line with similar rulings from the high court, which so far has not halted an execution based on a state's refusal to reveal its lethal injection drug supplier.

Death penalty states have been scrambling to find drugs after several manufacturers refused to sell their products for use in lethal injections.

The secrecy argument also was used by lawyers ahead of a bungled execution in April in Oklahoma, though that inmate's faulty veins, not the drug, have been cited as the likely culprit.

Two weeks ago, the Texas Attorney General's office, ruling in an open records case from attorneys for a death row inmate, said Texas can keep its execution drug supplier secret. The ruling cited arguments from law enforcement that suppliers face serious danger if they are identified.

Lawyers for death row inmates insist they need the information to verify the drugs' potency and protect inmates from unconstitutionally cruel and unusual punishment.

In another case Monday, the Supreme Court refused to consider an appeal from a man sent to Texas death row for strangling and trying to rape a woman jogging on a trail near her Houston home nearly 17 years ago.

Arthur Lee Burton, 44, had appealed a lower court's rejection of his arguments that his admission to a prison sociologist that he killed Nancy Adleman, a 48-year-old mother of three, was improperly obtained. Burton's original sentence was thrown out by the Texas Court of Criminal Appeals. He received another death sentence at a new punishment trial in 2002.

Burton also had argued his legal help at his trial and in earlier appeals was deficient.

In the third case, the high court upheld the murder conviction and death sentence given to a Fort Worth man, Kwame Rockwell, for a 2010 convenience store holdup that left two men dead. Rockwell, now 38, was convicted in 2012 of the fatal shooting of Daniel Rojas, 22, a clerk at a southeast Fort Worth store. Evidence showed a 70-year-old deliveryman, Jerry Burnett, also was fatally shot.

None of the three -- Campbell, Burton or Rockwell -- has an execution date.